Why lines seen in Texture Paint
This issue is caused due to the UV edges touching both the black background and the green paint
It also helps when you use a mipmap as the resolution decreases.

To fix this you need to draw a bit over the UV border. This creates something like a padding. 

Another way would be to match the background and the colored areas as close as possible.

Additionally a clean UV unwrap would also help a lot as it reduces the ammount of these edge areas.